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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 461 · 40 sums
TalentJR

The trick (Paravartya Yojayet): For ax + by = c and dx + ey = f: bottom = a×e − b×d. x = (c×e − b×f) ÷ bottom; y = (a×f − c×d) ÷ bottom. Special case ax + by = c, bx + ay = f: add the equations to get x + y, subtract to get x − y, then add and halve. Check your x and y in the first equation.

NameDateTime takenScore ___ / 40
  1. 1.4x + 2y = 30 and 2x + 4y = 6 →
  2. 2.4x + 3y = −23 and 3x + 4y = −26 →
  3. 3.3x + 5y = 11 and 5x + 3y = −3 →
  4. 4.4x + 2y = −10 and 5x − 2y = −26 →
  5. 5.6x + 2y = 10 and 6x − 3y = 30 →
  6. 6.4x + 6y = −6 and 3x − 4y = −30 →
  7. 7.4x + 3y = −6 and 5x − 4y = −54 →
  8. 8.3x + 2y = 21 and x − 3y = −26 →
  9. 9.2x + y = −13 and x − 5y = 32 →
  10. 10.7x + 2y = −14 and 2x + 7y = 41 →
  11. 11.2x + 7y = 31 and 7x + 2y = −4 →
  12. 12.6x + 5y = 8 and 5x + 6y = 3 →
  13. 13.5x − 4y = 41 and x − 4y = 37 →
  14. 14.5x + 6y = 53 and 3x + y = 24 →
  15. 15.9x + y = −81 and x + 9y = −89 →
  16. 16.5x − y = 10 and 6x − 4y = 26 →
  17. 17.x − 4y = 11 and 3x − 2y = 23 →
  18. 18.3x − 2y = −11 and 6x + 4y = −14 →
  19. 19.x + 9y = 68 and 9x + y = 52 →
  20. 20.5x − 5y = −50 and x + 2y = 2 →
  21. 21.9x + y = −46 and x + 9y = 66 →
  22. 22.5x + 2y = 49 and 4x + 4y = 56 →
  23. 23.9x + 4y = −27 and 4x + 9y = 53 →
  24. 24.6x + 3y = 18 and 3x + 6y = −27 →
  25. 25.x − 2y = 13 and 3x + 5y = 6 →
  26. 26.4x + 2y = 20 and x + 5y = 23 →
  27. 27.2x + 9y = 80 and 9x + 2y = 52 →
  28. 28.6x + 5y = 34 and x − 5y = −6 →
  29. 29.9x + 3y = −27 and 3x + 9y = −33 →
  30. 30.4x + 3y = 3 and 4x − 4y = −32 →
  31. 31.2x + 7y = −35 and 7x + 2y = 35 →
  32. 32.2x + 6y = −42 and 6x + 2y = −30 →
  33. 33.6x + 6y = −96 and 6x + 5y = −87 →
  34. 34.2x − y = 12 and 6x + 3y = 72 →
  35. 35.8x + 9y = 41 and 9x + 8y = 44 →
  36. 36.3x + 2y = 19 and 2x + 3y = 26 →
  37. 37.5x + 2y = −34 and 3x + 4y = −26 →
  38. 38.x − 3y = −4 and x + 3y = 2 →
  39. 39.5x + 6y = 38 and 6x − y = 21 →
  40. 40.5x + 4y = −43 and 4x + 5y = −47 →

Answer key

  1. x = 9, y = −3
  2. x = −2, y = −5
  3. x = −3, y = 4
  4. x = −4, y = 3
  5. x = 3, y = −4
  6. x = −6, y = 3
  7. x = −6, y = 6
  8. x = 1, y = 9
  9. x = −3, y = −7
  10. x = −4, y = 7
  11. x = −2, y = 5
  12. x = 3, y = −2
  13. x = 1, y = −9
  14. x = 7, y = 3
  15. x = −8, y = −9
  16. x = 1, y = −5
  17. x = 7, y = −1
  18. x = −3, y = 1
  19. x = 5, y = 7
  20. x = −6, y = 4
  21. x = −6, y = 8
  22. x = 7, y = 7
  23. x = −7, y = 9
  24. x = 7, y = −8
  25. x = 7, y = −3
  26. x = 3, y = 4
  27. x = 4, y = 8
  28. x = 4, y = 2
  29. x = −2, y = −3
  30. x = −3, y = 5
  31. x = 7, y = −7
  32. x = −3, y = −6
  33. x = −7, y = −9
  34. x = 9, y = 6
  35. x = 4, y = 1
  36. x = 1, y = 8
  37. x = −6, y = −2
  38. x = −1, y = 1
  39. x = 4, y = 3
  40. x = −3, y = −7

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